Method and system to assess disease using phase space tomography and machine learning

ABSTRACT

The exemplified intrinsic phase space tomography methods and systems facilitate the analysis and evaluation of complex, quasi-periodic system by generating computed phase-space tomographic images as a representation of the dynamics of the quasi-periodic cardiac systems. The computed phase-space tomographic images can be presented to a physician to assist in the assessment of presence or non-presence of disease. In some embodiments, the phase space tomographic images are used as input to a trained neural network classifier configured to assess for presence or non-presence of significant coronary artery disease.

RELATED APPLICATIONS

This application claims to, and the benefit of, U.S. Provisional Appl.No. 62/612,130, filed Dec. 29, 2017, titled “Method and System to AssessDisease Using Phase Space Tomography and Machine Learning,” which isincorporated by reference herein in its entirety.

FIELD OF THE INVENTION

The present disclosure generally relates to non-invasive methods andsystems for characterizing cardiovascular circulation and otherphysiological systems. More specifically, in an aspect, the presentdisclosure relates to non-invasive methods that utilize phase space datato generate a phase space tomographic images from an acquiredbiophysical signal (e.g., a cardiac signal, a brain/neurological signal,signals associated with other biological systems, etc.), in particular,to be used in the prediction and localization of coronary arterystenosis of the myocardium and characterize myocardial ischemia, amongother cardiac and non-cardiac disease and pathologies.

BACKGROUND

Ischemic heart disease, or myocardial ischemia, is a disease or group ofdiseases characterized by reduced blood supply of the heart muscle,usually due to coronary artery disease (CAD). CAD typically can occurwhen the lining inside the coronary arteries that supply blood to themyocardium, or heart muscle, develops atherosclerosis (the hardening orstiffening of the lining and the accumulation of plaque therein, oftenaccompanied by abnormal inflammation). Over time, CAD can also weakenthe heart muscle and contribute to, e.g., angina, myocardial infarction(cardiac arrest), heart failure, and arrhythmias. An arrhythmia is anabnormal heart rhythm and can include any change from the normalsequence of electrical conduction of the heart and in some cases canlead to cardiac arrest.

The evaluation of CAD can be complex, and many techniques and tools areused to assess the presence and severity of the condition. In the caseof electrocardiography, a field of cardiology in which the heart'selectrical activity is analyzed to obtain information about itsstructure and function, significant ischemic heart disease can alterventricular conduction properties of the myocardium in the perfusion beddownstream of the coronary artery narrowing or occlusion. This pathologycan express itself at different locations of the heart and at differentstages of severity, making an accurate diagnosis challenging. Further,the electrical conduction characteristics of the myocardium may varyfrom person to person, and other factors such as measurement variabilityassociated with the placement of measurement probes and parasitic lossesassociated with such probes and their related components can also affectthe biophysical signals that are captured during electrophysiologictests of the heart. Further still, when conduction properties of themyocardium are captured as relatively long cardiac phase gradientsignals, they may exhibit complex nonlinear variability that cannot beefficiently captured by traditional modeling techniques.

There is a benefit to having additional tools to non-invasively evaluatecoronary artery disease and other cardiac disease, neurological disease,and other disease of other physiological systems.

SUMMARY

The exemplified intrinsic phase space tomography methods and systemsfacilitate the analysis and evaluation of complex, quasi-periodic systemby generating tomographic images as a representation of the dynamics ofthe quasi-periodic cardiac systems. Indeed electrical conductionpatterns of the heart, or other acquired biophysical signals of otherorgans, can be represented as phase space tomographic images generatedas views of a phase space volumetric object (also referred to as a phasespace model) that has both a volumetric structure (e.g., a threedimensional structure) and/or a color map. In some embodiments, thephase space tomographic images are presented as two-dimensional views ofthe phase space volumetric object to assist a physician in theassessment of presence or non-presence of disease. In other embodiments,the phase space tomographic image is presented as a three-dimensionalrepresentation of the phase space volumetric object. In someembodiments, the phase space tomographic images are used as input to atrained neural network classifier configured to assess for presence ornon-presence of significant coronary artery disease. The phase spacetomographic images and outputs of the classifier can be presented to aphysician to assist in the assessment of presence or non-presence ofdisease. The exemplified methods and systems represents a new andefficient technique of assessing the presence of obstructive coronarylesions among other disease and pathologies.

In some embodiments, the methods and systems involve generating anoiseless subspace representation of a signal in three dimensions.Noiseless subspaces allow the observation of phase information oforthogonal leads that carries information about the structure of theheart and generates geometrical contrast in an image. This geometriccontrast is caused by different bioelectric structures having differentimpedances, and so spectral and non-spectral conduction delays bend thetrajectory of phase space orbit through the heart by different amounts.These small changes in trajectory can be normalized and quantified beatto beat and are represented in our model by the 20% lowest energyfrequency subspace. Normalized phase space differentials of the lowenergy subspace are mapped to form the vertices of a geometric mesh forvisualization. The mesh is then colored by the difference between themodel and the original signal. The result is the three-dimensional phasespace volumetric object which can be evaluated via a trained neuralnetwork classifier to produce the phase space tomographic image.

In some embodiments, contours and heat map of the tomographic images orof the assessed classifiers are generated and presented, separately oroverlaid over the tomographic images or over the assessed classifier, toaid a physician in the evaluation of the acquired data. The tomographicimages can be evaluated by physician alongside with results of amachine-generated formula to allow the physician an opportunity to makea more informed judgement of the results.

In some embodiments, the features of the volumetric structure and/or acolor map of the phase space tomographic images are extracted andevaluated to assess for the presence and/or absence of pathologies,e.g., ischemia relating to significant coronary arterial disease (CAD).In some embodiments, the phase space volumetric object can be assessedto extract topographic and geometric parameters, e.g., in a tomographicanalysis, that are used in models that determine indications of presenceor non-presence of significant coronary artery disease.

As used herein, the term “cardiac signal” refers to one or more signalsassociated with the structure, function and/or activity of thecardiovascular system—including aspects of that signal'selectrical/electrochemical conduction—that, e.g., cause contraction ofthe myocardium. A cardiac signal may include, in some embodiments,electrocardiographic signals such as, e.g., those acquired via anelectrocardiogram (ECG) or other modalities.

As used herein, the term “neurological signal” refers to one or moresignals associated with the structure, function and/or activity of thecentral and peripheral nervous systems, including the brain, spinalcord, nerves, and their associated neurons and other structures, etc.,and including aspects of that signal's electrical/electrochemicalconduction. A neurological signal may include, in some embodiments,electroencephalographic signals such as, e.g., those acquired via anelectroencephalogram (EEG) or other modalities.

As used herein, the term “biophysical signal” is not meant to be limitedto a cardiac signal and/or a neurological signal but encompasses anyphysiological signal from which information may be obtained. Notintending to be limited by example, one may classify biophysical signalsinto types or categories that can include, for example, electrical(e.g., certain cardiac and neurological system-related signals that canbe observed, identified and/or quantified by techniques such as themeasurement of voltage/potential, impedance, resistivity, conductivity,current, etc. in various domains such as time and/or frequency),magnetic, electromagnetic, optical (e.g. signals that can be observed,identified and/or quantified by techniques such as reflectance,interferometry, spectroscopy, absorbance, transmissivity, visualobservation and the like), acoustic, chemical, mechanical (e.g., signalsrelated to fluid flow, pressure, motion, vibration, displacement,strain), thermal, and electrochemical (e.g. signals that can becorrelated to the presence of certain analytes, such as glucose).Biophysical signals may in some cases be described in the context of aphysiological system (e.g., respiratory, circulatory (cardiovascular,pulmonary), nervous, lymphatic, endocrine, digestive, excretory,muscular, skeletal, renal/urinary/excretory, immune,integumentary/exocrine and reproductive systems), an organ system (e.g.,signals that may be unique to the heart and lungs as they worktogether), or in the context of tissue (e.g., muscle, fat, nerves,connective tissue, bone), cells, organelles, molecules (e.g., water,proteins, fats, carbohydrates, gases, free radicals, inorganic ions,minerals, acids, and other compounds, elements and their subatomiccomponents. Unless stated otherwise, the term “biophysical signalacquisition” generally refers to any passive or active means ofacquiring a biophysical signal from a physiological system, such as amammalian or non-mammalian organism. Passive biophysical signalacquisition generally refers to the observation of natural electrical,magnetic, and/or acoustics emittance of the body tissue. Non-limitingexamples of passive biophysical signal acquisition means includes, e.g.,voltage/potential, current, magnetic, acoustic, optical, and othernon-active ways of observing the natural emittance of the body tissue.Non-limiting examples of active biophysical signal acquisition meansinclude, e.g., ultrasound, radio waves, microwaves, infrared and/orvisible light (e.g., for use in pulse oximetry), visible light,ultraviolet light and other ways of actively interrogating the bodytissue that does not involve ionizing energy or radiation (e.g., X-ray).Active biophysical signal acquisition means that involves ionizingenergy or radiation (e.g., X-ray) are referred to as “ionizingbiophysical signal”, which can be acquired invasively (e.g., via surgeryor invasive radiologic intervention protocols) or non-invasively (e.g.,via imaging).

In an aspect, a method is disclosed for non-invasively assessingpresence or non-presence of significant coronary artery disease. Themethod includes obtaining, by one or more processors (e.g., from astored database or from a measurement equipment), acquired data from ameasurement of one more biophysical signals of a subject (e.g.,biopotential-based signals, ultrasound-based signals, magnetic-basedsignals), wherein the acquired data is derived from measurementsacquired via noninvasive equipment configured to measure properties(e.g., electric properties, magnetic properties, acoustic properties,impedance properties, and etc.) of the heart; and generating, by the oneor more processors, a set of tomographic images derived from a phasespace model generated based on the acquired data, wherein at least oneof the phase space model comprises a plurality of faces and a pluralityof vertices, wherein the plurality of vertices are defined, in part, bya fractional subspace derivative operation and by low-energy subspaceparameters generated directly or indirectly from the acquired data(e.g., wherein the position values of the vertices are based onlow-energy subspace parameters determined from a model-derivedreconstruction operation); wherein the set of tomographic images arepresented (e.g., on a local or a remote computing system) for theassessment of presence and/or non-presence of significant coronaryartery disease.

In some embodiments, the method includes determining, by the one or moreprocessors, a machine-trained assessment of presence and/or non-presenceof significant coronary artery disease using a trained neuralnetwork-based nonlinear classifier configured to map individual pixelsof the tomographic images to a binary predictor.

In some embodiments, the method includes generating a contour data setfor each tomographic image of the set of tomographic images, wherein thecontour data are presented for the assessment of presence and/ornon-presence of significant coronary artery disease.

In some embodiments, the contour data set is generated by sweeping, viathe one or more processors, a moving window associated with the trainedneural network-based nonlinear classifier on a pixel by pixel basisover, at least a portion of, a given tomographic image; and combining,for a given pixel of the tomographic image, outputs of the swept movingwindow.

In some embodiments, the method includes presenting, via a display of aremote computing system, the generated contour data set.

In some embodiments, the method includes presenting, via the display ofthe remote computing system, the generated contour data set and acorresponding tomographic image used to generate the contour data set,wherein the generated contour data set is rendered as an overlay overthe corresponding tomographic image.

In some embodiments, the generated contour data set comprises color mapdata.

In some embodiments, the method includes presenting, via a display ofthe remote computing system, the set of tomographic images inconjunction with the generating a contour data set.

In some embodiments, the vertices and faces of the generated phase spacemodel comprises color data, the steps of generating the tomographicimages comprising converting the generated phase space model togreyscale.

In some embodiments, the tomographic images are generated by generatinga plurality of images corresponding to a plurality of orientation of thegenerated phase space model, wherein the image are generated at a firstimage resolution; and converting the plurality of images to a secondimage resolution, wherein the second image resolution is different fromthe first image resolution (e.g., wherein the second image resolutionhas a lower number of pixels as compared to the first image resolution).

In another aspect, a method is disclosed for non-invasively measuringmyocardial ischemia (determining presence thereof; determininglocation(s) thereof and/or areas impacted by condition; and/ordetermining a degree thereof), measuring one or more stenoses (e.g.,determining presence thereof; and/or determining localization thereof;and/or determining a degree thereof), or measuring fractional flowreserve (e.g., estimating value thereof at an identified stenosis). Themethod includes obtaining, by one or more processors, acquired data froma measurement of one more electrical signals of a subject (e.g.,biopotential-based signals, ultrasound-based signals, magnetic-basedsignals), wherein the acquired data is derived from measurementsacquired via noninvasive equipment configured to measure properties(e.g., electric properties, magnetic properties, acoustic properties,impedance properties, and etc.) of the heart; generating, by the one ormore processors, one or more phase space models (e.g., phase spacevolumetric objects) based on the acquired data, wherein at least one ofthe one or more phase space models comprises a plurality of faces and aplurality of vertices, wherein the plurality of vertices are defined, inpart, by fractional subspace derivative operations of low-energysubspace parameters generated directly or indirectly from the acquireddata; and determining, by the one or more processors, one or morecoronary physiological parameters of the subject selected from the groupconsisting of a fractional flow reserve estimation, a stenosis value,and a myocardial ischemia estimation, based on the generated phase spacevolumetric object (e.g., and causing, by the one or more processors,output of the one or more coronary physiological parameters (e.g., in areport, a display, instrumentation output, etc.)).

In some embodiments, the generated phase space volumetric objectcomprises a three-dimensional object defined by the plurality of facesand a plurality of vertices.

In some embodiments, the plurality of vertices are generated as a pointcloud in 3D space (e.g., having X, Y, and Z components), wherein eachpoint in the point cloud has a value (e.g., color value) associated witha fractional order of a fractional subspace derivative operation of thelow-energy subspace parameters (e.g., wherein a fractional subspacederivative operation of the low-energy subspace parameters for a givenfractional order generates a 2D data set).

In some embodiments, each fractional order of the fractional subspacederivative operation is predetermined and corresponds to a frequency, ora range thereof, of electrical conduction events of the heart includingthose associated with activation (e.g., ventricular and/or atriodepolarization) of the various chambers and recovery (i.e., ventricularand/or atrio repolarization).

In some embodiments, each of the plurality of vertices or each of theplurality of faces comprises one or more attribute parameters (e.g.,color).

In some embodiments, each of the plurality of vertices or each of theplurality of faces comprises one or more color attribute parameters.

In some embodiments, at least one of the one or more color attributeparameters is associated with a variance of a modeled channel signalgenerated from a model-derived construction (e.g., a sparseapproximation algorithm such as, or based on, principal componentanalysis (PCA), matching pursuit, orthogonal matching pursuit,orthogonal search, projection pursuit, LASSO, fast orthogonal search,Sparse Karhunen-Loeve Transform, and combinations thereof) of theacquired data subtracted from a baseline-removed raw channel of theacquired data.

In some embodiments, the plurality of faces are generated from atriangulation operation of the plurality of vertices.

In some embodiments, the plurality of faces are generated from thetriangulation operation, the triangulation operation being selected fromthe group consisting of Delaunay triangulation, Mesh generation, AlphaHull triangulation, and Convex Hull triangulation.

In some embodiments, each of the plurality of faces comprises one ormore face attribute parameters (e.g., color).

In some embodiments, each of the plurality of faces comprises one ormore face color attribute parameters.

In some embodiments, at least one of the one or more face colorattribute parameters is a triangular interpolation among bounding vertexattribute parameters (e.g., 3 bound vertex colors).

In some embodiments, the fractional order is a rational number or anirrational number associated with one or more linear and/or non-lineardynamic response of the heart.

In some embodiments, the method further includes removing, by the one ormore processors, a baseline wandering trend from the acquired data priorto generating the one or more phase space models.

In some embodiments, the method further includes performing amodel-derive reconstruction operation of the acquired data to generatethe low-energy subspace parameters, the low-energy subspace parameterscomprising a plurality of basis functions and coefficients (e.g., alinear combination of plurality of basis functions scaled by one or morecoefficients).

In some embodiments, the low-energy subspace parameters consist oflow-energy subsets of plurality of basis functions and coefficients.

In some embodiments, the low-energy subsets of plurality of basisfunctions and coefficients are selected from the group consisting of:about 1% of plurality of basis functions and coefficients associatedwith low energy frequency subspace; about 5% of plurality of basisfunctions and coefficients associated with low energy frequencysubspace; about 10% of plurality of basis functions and coefficientsassociated with low energy frequency subspace; about 15% of plurality ofbasis functions and coefficients associated with low energy frequencysubspace; about 20% of plurality of basis functions and coefficientsassociated with low energy frequency subspace; and about 25% ofplurality of basis functions and coefficients associated with low energyfrequency subspace.

In some embodiments, the model-derived reconstruction operationgenerates over 100 basis functions and coefficients for a given acquireddata.

In some embodiments, parameters associated with generated one or morephase space models are used in subsequent machine learning operations(e.g., image-based machine learning operations or feature-based machinelearning operations) to determine the one or more coronary physiologicalparameters.

In some embodiments, the parameters associated with generated one ormore phase space models are associated with geometric properties of thegenerated one or more phase space models.

In some embodiments, the parameters associated with generated one ormore phase space models are associated with geometric properties of thegenerated one or more phase space models selected from the groupconsisting of volume, number of distinct bodies, and color gradient.

In some embodiments, the method further includes causing, by the one ormore processors, generation of a visualization of generated phase spacevolumetric model as a three-dimensional object, wherein thethree-dimensional object is rendered and displayed at a display of acomputing device (e.g., computing workstation; a surgical, diagnostic,or instrumentation equipment).

In some embodiments, the method further includes causing, by the one ormore processors, generation of a visualization of generated phase spacevolumetric model as a three-dimensional object, wherein thethree-dimensional object is displayed in a report (e.g., an electronicreport).

In some embodiments, the acquired data comprises differential channelsignals (e.g., 3 sets of differential measurement simultaneouslysampled; or 6 sets of unipolar measurements simultaneously sampled).

In some embodiments, the acquired data comprise signals associated withinterference (e.g., in phase plane) of depolarization waves amongorthogonal leads.

In some embodiments, the method further includes extracting a first setof morphologic features of the generated phase space volumetric model,wherein the first set of extracted morphologic features includeparameters selected from the group consisting of a 3D volume value, avoid volume value, a surface area value, a principal curvature directionvalue, and a Betti number value.

In some embodiments, the method further includes dividing the generatedphase space volumetric model into a plurality of segments eachcomprising non-overlapping portions of the generated phase spacevolumetric model; and extracting a set of morphologic features of eachof the plurality of segments, wherein the second set of extractedmorphologic features includes parameters selected from the groupconsisting of a 3D volume value, a void volume value, a surface areavalue, a principal curvature direction value, and a Betti number value.

In some embodiments, the plurality of segments comprise a number ofsegments selected from the group consisting of 3, 4, 5, 6, 7, 8, 9, 10,11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

In some embodiments, the acquired data are acquired as one or morewide-band gradient signals simultaneously from the subject via at leastone electrode.

In some embodiments, at least one of one or more wide-band gradientsignals comprise a high-frequency time series data that is unfiltered(e.g., spectrally unmodified) prior to the processing in the phase-spaceanalysis.

In some embodiments, the one or more wide-band gradient signals comprisecardiac frequency information at a frequency selected from the groupconsisting of about 1 kHz, about 2 kHz, about 3 kHz, about 4 kHz, about5 kHz, about 6 kHz, about 7 kHz, about 8 kHz, about 9 kHz, about 10 kHz,and greater than 10 kHz (e.g., 0-50 kHz or 0-500 kHz).

In another aspect, a system is disclosed comprising a processor; and amemory having instructions thereon, wherein the instructions whenexecuted by the processor, cause the processor to perform any of theabove method.

In another aspect, a non-transitory computer readable medium isdisclosed having instructions stored thereon, wherein execution of theinstructions, cause the processor to perform any of the above method.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate embodiments and together with thedescription, serve to explain the principles of the methods and systems.The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

Embodiments of the present invention may be better understood from thefollowing detailed description when read in conjunction with theaccompanying drawings. Such embodiments, which are for illustrativepurposes only, depict novel and non-obvious aspects of the invention.The drawings include the following figures:

FIG. 1 is a diagram of an example system configured to assessnon-invasively presence or non-presence of a disease state (e.g.,significant coronary artery disease) using biophysical phase gradientcomputed tomography (also referred to herein as computed phase spacetomography), in accordance with an illustrative embodiment.

FIGS. 2 and 3 each shows a phase space volumetric object generated froma biophysical measurement of a subject determined to have significantcoronary artery disease in accordance with an illustrative embodiment.

FIG. 4 shows a phase space volumetric object generated from abiophysical measurement of a subject known to be CAD determined not tohave significant coronary artery disease in accordance with anillustrative embodiment.

FIG. 5 shows a phase space volumetric object generated from ameasurement of a subject determined to have significant coronary arterydisease in which the object includes an arc structure that forms an openspace in the object in accordance with an illustrative embodiment.

FIG. 6 is an example method of generating a phase space volumetricobject by the non-invasive cardiac assessment system in accordance withan illustrative embodiment.

FIG. 7 is a diagram of an exemplary method of processing thephase-gradient biophysical data set in accordance with an illustrativeembodiment.

FIG. 8 shows an image of a representation of a phase space volumetricobject generated from a signal collected from subject with no reportedarterial blockage in accordance with an illustrative embodiment.

FIGS. 9, 10, and 11 each shows an image of a representation of a phasespace volumetric object generated from a signal collected from a subjectdiagnosed with one or more reported arterial blockages only betweenabout 50% and about 65% in accordance with an illustrative embodiment.

FIGS. 12, 13, 14, 15, and 16 each shows an image of a representation ofa phase space volumetric object generated from a signal collected from asubject diagnosed with at least one reported arterial blockage greaterthan 70% in accordance with an illustrative embodiment.

FIGS. 17, 18, 19, 20, and 21 each shows an image of a representation ofa phase space volumetric object generated from a signal collected from asubject diagnosed with more than one reported arterial blockage eachgreater than 70% in accordance with an illustrative embodiment.

FIGS. 22A, 22B, 22C, 22D, 22E, and 22F show a set of computedphase-space tomographic images derived from different views of the phasespace volumetric object associated with a healthy subject in accordancewith an illustrative embodiment.

FIGS. 23A, 23B, 23C, 23D, 23E, and 23F show outputted classification ofthe tomographic images of FIGS. 22A-22F for presence and non-presence ofsignificant coronary artery disease determined via a neural networkclassifier, in accordance with an illustrative embodiment.

FIGS. 24A, 24B, 24C, 24D, 24E, and 24F show the outputted classificationof the tomographic images of FIGS. 22A-22F overlaid with a contour dataset and heat map associated with the classifier in accordance with anillustrative embodiment.

FIGS. 25A, 25B, 25C, 25D, 25E, and 25F show only the contour data setand heat map of FIGS. 24A-24F in accordance with an illustrativeembodiment.

FIGS. 26A, 26B, 26C, 26D, 26E, and 26F show computed phase-spacetomographic images derived from different views of the phase spacevolumetric object 112 and overlaid with the contour data set and heatmap data set generated from the neural network classifier of FIGS.25A-25F in accordance with an illustrative embodiment.

FIGS. 27A, 27B, 27C, 27D, 27E, and 27F show computed phase-spacetomographic images derived from different views of a phase spacevolumetric object 112 (shown as 112 b) associated with a subjectdiagnosed with significant coronary artery disease in accordance with anillustrative embodiment. The computed phase-space tomographic images areshown with contour data set and heat map data set generated from aneural network classifier applied to the computed phase-spacetomographic images.

FIGS. 28A, 28B, 28C, 28D, 28E, and 28F show outputted classification ofthe tomographic images of FIGS. 27A-27F for presence and non-presence ofsignificant coronary artery disease determined via a neural networkclassifier, in accordance with an illustrative embodiment.

FIGS. 29A, 29B, 29C, 29D, 29E, and 29F show example two dimensionaloverlay superimposed over a three-dimensional volumetric object inaccordance with an illustrative embodiment.

FIGS. 30A, 30B, 30C, 30D, 30E, and 30F show example three dimensionaloverlay superimposed over a three-dimensional volumetric object inaccordance with an illustrative embodiment.

FIG. 31 shows a table with characteristics of a development and testdata set used to train a neural network classifier in accordance with anillustrative embodiment.

FIGS. 32, 33, 34, 35, 36, 37, 38, and 39 show example graphical userinterface for a clinician web portal, or a report derived therefrom, toview and assess cardiac phase space tomographic images, in accordancewith an illustrative embodiment.

FIG. 40 shows an exemplary computing environment in which exampleembodiments of the assessment system 110 and aspects thereof may beimplemented.

DETAILED SPECIFICATION

Each and every feature described herein, and each and every combinationof two or more of such features, is included within the scope of thepresent invention provided that the features included in such acombination are not mutually inconsistent.

While the present disclosure is directed to the beneficial assessment ofbiophysical signals in the diagnosis and treatment of cardiac-relatedpathologies and conditions and/or neurological-related pathologies andconditions, such assessment can be applied to the diagnosis andtreatment (including, surgical, minimally invasive, and/or pharmacologictreatment) of any pathologies or conditions in which a biophysicalsignal is involved in any relevant system of a living body. One examplein the cardiac context is the diagnosis of CAD and its treatment by anynumber of therapies, alone or in combination, such as the placement of astent in a coronary artery, performance of an atherectomy, angioplasty,prescription of drug therapy, and/or the prescription of exercise,nutritional and other lifestyle changes, etc. Other cardiac-relatedpathologies or conditions that may be diagnosed include, e.g.,arrhythmia, congestive heart failure, valve failure, pulmonaryhypertension (e.g., pulmonary arterial hypertension, pulmonaryhypertension due to left heart disease, pulmonary hypertension due tolung disease, pulmonary hypertension due to chronic blood clots, andpulmonary hypertension due to other disease such as blood or otherdisorders), as well as other cardiac-related pathologies, conditionsand/or diseases. Non-limiting examples of neurological-related diseases,pathologies or conditions that may be diagnosed include, e.g., epilepsy,schizophrenia, Parkinson's Disease, Alzheimer's Disease (and all otherforms of dementia), autism spectrum (including Asperger syndrome),attention deficit hyperactivity disorder, Huntington's Disease, musculardystrophy, depression, bipolar disorder, brain/spinal cord tumors(malignant and benign), movement disorders, cognitive impairment, speechimpairment, various psychoses, brain/spinal cord/nerve injury, chronictraumatic encephalopathy, cluster headaches, migraine headaches,neuropathy (in its various forms, including peripheral neuropathy),phantom limb/pain, chronic fatigue syndrome, acute and/or chronic pain(including back pain, failed back surgery syndrome, etc.), dyskinesia,anxiety disorders, conditions caused by infections or foreign agents(e.g., Lyme disease, encephalitis, rabies), narcolepsy and other sleepdisorders, post-traumatic stress disorder, neurologicalconditions/effects related to stroke, aneurysms, hemorrhagic injury,etc., tinnitus and other hearing-related diseases/conditions andvision-related diseases/conditions.

Example System

FIG. 1 is a diagram of an example system 100 configured to assess (e.g.,non-invasively assess) presence or non-presence of a disease state(e.g., significant coronary artery disease) in a physiological system ofa subject using cardiac phase gradient computed tomography (alsoreferred to as computed phase space tomography), in accordance with anillustrative embodiment. As noted herein, physiological systems canrefer to the cardiovascular system, the pulmonary system, the renalsystem, the nervous system, and other functional systems and sub-systemsof the body. In the context of the cardiovascular system, the particularembodiment of the system 100 facilitates the investigation of complex,nonlinear systems of the heart by examining in phase space the states,or phases, that such a system may exhibit over many cycles.

In FIG. 1, measurement system 102 is a non-invasive embodiment (shown as“Measurement System (biophysical)” 102) that acquires a plurality ofbiophysical signals 104 (e.g., phase gradient biophysical signals) viameasurement probes 114 (shown as probes 114 a, 114 b, 114 c, 114 d, 114e, and 114 f) from a subject 106 to produce a phase-gradient biophysicaldata set 108. Assessment system 110 (shown as “Non-invasive assessmentsystem” 110) receives the phase-gradient biophysical data set 108 andgenerates one or more phase space volumetric objects 112 (also referredto herein as a “phase space volumetric model” 112) for analysis of thephase-gradient biophysical data set 108. Each of the phase spacevolumetric objects 112 as a three-dimensional structure includes aplurality of vertices generated as a point cloud in three-dimensionalspace and a plurality of faces defined by the plurality of vertices. Theassessment system 110 can further determine, in some embodiments, a setof computed phase space tomographic images from the phase spacevolumetric objects 112. A machine learned classifier can be applied onthe computed phase space tomographic images or the computed phasegradient tomographic images from which the images are derived to assessthe contextual information on cardiac health. The color and shape of thephase space volumetric objects 112 and computed phase space tomographicimages derived therefrom beneficially synthesize and display theelectrical and functional characteristics of the heart.

In FIG. 1, system 100, in some embodiments, includes a healthcareprovider portal (shown as “Portal” 128) configured to display storedphase space volumetric objects 112 or images derived therefrom (amongother intermediate data sets) in a phase space tomographic and/orangiographic-equivalent report. Portal 128, which in some embodimentsmay be termed a physician or clinician portal 128, is configured toaccess, retrieve, and/or display or present reports and/or the phasespace tomographic volumetric images (and other data) for the report)from a repository (e.g., a storage area network).

In some embodiments, and as shown in FIG. 1, the healthcare providerportal 128 is configured to display phase space volumetric objects 112or images derived therefrom in, or along with, an anatomical mappingreport, a coronary tree report, and/or a 17-segment report. Portal 128may present depictions of rotatable and optionally scalablethree-dimensional phase space volumetric objects 112 or images derivedtherefrom. Portal 128 may present the data, e.g., in real-time (e.g., asa web object), as an electronic document, and/or in other standardizedor non-standardized image visualization/medical datavisualization/scientific data visualization formats. The anatomicalmapping report, in some embodiments, includes one or more depictions ofa rotatable and optionally scalable three-dimensional anatomical map ofcardiac regions of affected myocardium. The anatomical mapping report,in some embodiments, is configured to display and switch between a setof one or more three-dimensional views and/or a set of two-dimensionalviews of a model having identified regions of myocardium. The coronarytree report, in some embodiments, includes one or more two-dimensionalview of the major coronary artery. The 17-segment report, in someembodiments, includes one or more two-dimensional 17-segment views ofcorresponding regions of myocardium. In each of the report, the valuethat indicates presence of cardiac disease or condition at a location inthe myocardium, as well as a label indicating presence of cardiacdisease, may be rendered as both static and dynamic visualizationelements that indicates area of predicted blockage, for example, withcolor highlights of a region of affected myocardium and with ananimation sequence that highlight region of affected coronaryarter(ies). In some embodiments, each of the report includes textuallabel to indicate presence or non-presence of cardiac disease (e.g.,presence of significant coronary artery disease) as well as a textuallabel to indicate presence (i.e., location) of the cardiac disease in agiven coronary artery disease.

In some embodiments, the Portal 128 is configured to display phase spacevolumetric objects 112 and/or stored phase space tomographic volumetricimages (among other intermediate data sets) in the phase spacetomographic and/or angiographic-equivalent report. The physician orclinician portal 128, in some embodiments, is configured to access andretrieve reports or the phase space tomographic volumetric images (andother data) for the report) from a repository (e.g., a storage areanetwork). The physician or clinician portal 128 and/or repository can becompliant with patient information and other personal data privacy lawsand regulations (such as, e.g., the U.S. Health Insurance Portabilityand Accountability Act of 1996 and the EU General Data ProtectionRegulation) and laws relating to the marketing of medical devices (suchas, e.g., the US Federal Food and Drug Act and the EU Medical DeviceRegulation).. Further description of an example healthcare providerportal 128 is provided in U.S. Publication No. 2018/0078146, title“Method and System for Visualization of Heart Tissue at Risk”, which isincorporated by reference herein in its entirety. Although in certainembodiments, Portal 128 is configured for presentation of patientmedical information to healthcare professionals, in other embodiments,the healthcare provider portal 128 can be made accessible to patients,researchers, academics, and/or other portal users.

In the context of cardiovascular systems, in some embodiments, thehealthcare provider portal (and corresponding user interface) 128 isconfigured to present summary information visualizations of myocardialtissue that identifies myocardium at risk and/or coronary arteries thatare blocked. The user interface can be a graphical user interface(“GUI”) with a touch- or pre-touch sensitive screen with inputcapability. The user interface can be used, for example, to directdiagnostics and treatment of a patient and/or to assess patients in astudy. The visualizations, for a given report of a study, may includemultiple depictions of a rotatable three-dimensional anatomical map ofcardiac regions of affected myocardium, a corresponding two-dimensionalview of the major coronary arteries, and a corresponding two-dimensional17-segment view of the major coronary arteries to facilitateinterpretation and assessment of architectural features of themyocardium for characterizing abnormalities in the heart and incardiovascular functions.

The measurement system 102, in some embodiments, is configured toacquire biophysical signals that may be based on the body's biopotentialvia biopotential sensing circuitries as biopotential biophysicalsignals. In the cardiac and/or electrocardiography contexts, measurementsystem 102 is configured to capture cardiac-related biopotential orelectrophysiological signals of a living organism (such as a human) as abiopotential cardiac signal data set. In some embodiments, measurementsystem 102 is configured to acquire a wide-band cardiac phase gradientsignals as a biopotential signal or other signal types (e.g., a currentsignal, an impedance signal, a magnetic signal, an optical signal, anultrasound or acoustic signal, etc.). The term “wide-band” in referenceto an acquired signal, and its corresponding data set, refers to thesignal having a frequency range that is substantially greater than theNyquist sampling rate of the highest dominant frequency of aphysiological system of interest. For cardiac signals, which typicallyhave dominant frequency components between about 0.5 Hz and about 80 Hz,the wide-band cardiac phase gradient signals or wide-band cardiacbiophysical signals comprise cardiac frequency information at afrequency selected from the group consisting between about 0.1 Hz andabout 1 KHz, between about 0.1 Hz and about 2 KHz, between about 0.1 Hzand about 3 KHz, between about 0.1 Hz and about 4 KHz, between about 0.1Hz and about 5 KHz, between about 0.1 Hz and about 6 KHz, between about0.1 Hz and about 7 KHz, between about 0.1 Hz and about 8 KHz, betweenabout 0.1 Hz and about 9 KHz, between about 0.1 Hz and about 10 KHz, andbetween about 0.1 Hz and greater than 10 KHz (e.g., 0.1 Hz to 50 KHz or0.1 Hz to 500 KHz). In addition to capturing the dominant frequencycomponents, the wide-band acquisition also facilitate capture of otherfrequencies of interest. Examples of such frequencies of interest caninclude QRS frequency profiles (which can have frequency ranges up toabout 250 Hz), among others. The term “phase gradient” in reference toan acquired signal, and its corresponding data set, refers to the signalbeing acquired at different vantage points of the body to observe phaseinformation for a set of distinct events/functions of the physiologicalsystem of interest. Following the signal acquisition, the term “phasegradient” refers to the preservation of phase information via use ofnon-distorting signal processing and pre-processing hardware, software,and techniques (e.g., phase-linear filters and signal-processingoperators and/or algorithms).

In the neurological context, measurement system 102 is configured tocapture neurological-related biopotential or electrophysiologicalsignals of a living subject (such as a human) as a neurologicalbiophysical signal data set. In some embodiments, measurement system 102is configured to acquire wide-band neurological phase gradient signalsas a biopotential signal or other signal types (e.g., a current signal,an impedance signal, a magnetic signal, an ultrasound, an opticalsignal, an ultrasound or acoustic signal, etc.). Examples of measurementsystem 102 are described in U.S. Publication No. 2017/0119272 and inU.S. Publication No. 2018/0249960, each of which is incorporated byreference herein in its entirety.

In some embodiments, measurement system 102 is configured to capturewide-band biopotential biophysical phase gradient signals as unfilteredelectrophysiological signals such that the spectral component(s) of thesignals are not altered. Indeed, in such embodiments, the wide-bandbiopotential biophysical phase gradient signals are captured, converted,and even analyzed without having been filtered (via, e.g., hardwarecircuitry and/or digital signal processing techniques, etc.) (e.g.,prior to digitization) that otherwise can affect the phase linearity ofthe biophysical signal of interest. In some embodiments, the wide-bandbiopotential biophysical phase gradient signals are captured inmicrovolt or sub-microvolt resolutions that are at, or significantlybelow, the noise floor of conventional electrocardiographic,electroencephalographic, and other biophysical-signal acquisitioninstruments. In some embodiments, the wide-band biopotential biophysicalsignals are simultaneously sampled having a temporal skew or “lag” ofless than about 1 microseconds, and in other embodiments, having atemporal skew or lag of not more than about 10 femtoseconds. Notably,the exemplified system minimizes non-linear distortions (e.g., thosethat can be introduced via certain filters) in the acquired wide-bandphase gradient signal to not affect the information therein.

Referring still to FIG. 1, the plurality of vertices of the phase spacevolumetric object is spatially defined, in some embodiments, by thesubspace data set (e.g., a low-energy frequency subspace data set) of athree dimensional phase space model generated from the phase-gradientbiophysical data set 108. Further, each, or a substantial portion, ofthe plurality of vertices of the phase space volumetric object 112 hasone or more values (e.g., a color value) that correspond to a fractionalorder derivative operation as applied, for example, to, thephase-gradient biophysical data set 108, and/or the three dimensionalphase space model generated from the phase-gradient biophysical data set108. The three dimensional phase space model can be configured as a setof time series data of three sets of differential channel signalsderived from the phase-gradient biophysical data set 108. The fractionalderivative operations can be used, for instance, to compensate fornoise, lead placement errors and to create more accurate tissueimpedance models.

The phase space volumetric objects 112 includes a plurality of facesgenerated by a triangulation operation on the three-dimensional pointcloud. In some embodiments, the triangulation operation includes anAlpha Hull triangulation operation of the three-dimensional time-seriespoints in which a predetermined radius a is used to generate faces thatare mapped to the plurality of vertices. In other embodiments, Delaunaytriangulation, alpha shapes, ball pivoting, Mesh generation, Convex Hulltriangulation, and the like, is used.

As discussed in U.S. Publication No. 2013/0096394, which is incorporatedby reference herein in its entirety, a mathematical reconstruction ofthe phase-gradient biophysical data signal may comprise various elementsincluding, in some embodiments, an input/output (I/O) expansion of thephase-gradient biophysical data signal in which at least one of theterms of the I/O expansion are fractionally differentiable (e.g.,analytically fractionally differentiable). In some embodiments, the I/Oexpansion comprises a fractional integral of the mathematicalreconstruction. Sparse approximation operation comprises a set ofoperations, often iterative, to find a best matching projection of adata set (e.g., multi-dimensional data) onto candidate functions in adictionary. Each dictionary can be a family of waveforms that is used todecompose the input data set. The candidate functions, in someembodiments, are linearly combined to form a sparse representation ofthe input data set. These operations can be numerical or analytical. Insome embodiments, the mathematical reconstruction is based on principalcomponent analysis (PCA), matching pursuit, orthogonal matching pursuit,orthogonal search, projection pursuit, LASSO, fast orthogonal search,Sparse Karhunen-Loeve Transform, or combinations thereof. In otherembodiments, the I/O expansion comprises an irrational fractionalsubspace derivative of the mathematical reconstruction of thephase-gradient biophysical data signal. The recited examples are notexhaustive and other sparse approximation algorithms or methods may beused as well as any variations and combinations thereof.

As discussed in U.S. Publication No. 2013/0096394, there are a couple ofpoints about the low-energy component subspace (made from the last,e.g., 20% terms found by a matching pursuit reconstruction algorithmoperation) that are interesting and useful. First, the fractionalintegral and derivative of these components can be noiselesslydetermined, since it is a linear combination of selected candidateterms, and this fractional derivative can be useful to distinguishventricular tachycardia potential in post myocardial infarction patientsand those with congenital heart defects. In addition, there are someuseful fractional properties to consider. Thus suppose that x(t), y(t),and z(t) are respectively the X, Y, and Z coordinates of the low-energycomponent and let x_(a)(t), y_(a)(t), and z_(a)(t) be their irrationalfractional derivative of order a that can be any real or complex number.

In some embodiments, the fractional derivative operation is based onGrünwald-Letnikov fractional derivative method. In some embodiments, thefractional derivative operation is based on the Lubich's fractionallinear multi-step method. In some embodiments, the fractional derivativeoperation is based on the fractional Adams-Moulton method. In someembodiments, the fractional derivative operation is based on theRiemann-Liouville fractional derivative method. In some embodiments, thefractional derivative operation is based on Riesz fractional derivativemethod. Other methods of performing a fractional derivative may be used.

To predict presence or non-presence of significant coronary arterydisease from the phase-space tomographic images, a trained neuralnetwork is applied, in some embodiments, to a number of views (e.g., sixviews) of each tomographic image (e.g., top, bottom, front, back, leftand right view). In some embodiments, images acquired of thethree-dimensional volumetric object 112 is first converted to grayscaleand scaled to a pre-defined image resolution (e.g., 195×128 pixels).Other pixel count and image resolution can be used. In some embodiments,the neural network classifier includes multiple hidden neurons (e.g., 15hidden neurons) with leaky rectified linear activations. Dropout may beused between the hidden layer and the final output neuron to preventoverfitting. L1 and L2 regularization penalties may also be applied. Abinary cross entropy may be used as a loss function. Optimization may beperformed using the gradient-based Adam algorithm.

Heat maps and contour plots, in some embodiments, are generated from theoutputs of the neural network classifier on a given phase-spacetomographic image or from the computed phase space tomographic imagesthemselves. In some embodiments, a 4×4 moving window of white pixels(e.g., having a value of 1 in grayscale images) is swept over the entireimage, with the neural network classifier being evaluated once for eachwindow position and the output of the neural network being recorded.When a given pixel in the PST image is covered by the moving window morethan once (e.g., when the window is larger than a single pixel butmoving one pixel at a time), each pixel in the heat map may have a valuethat is an average output of the neural network classifier when thecorresponding pixel in the phase-space tomographic image is covered bythe window. Contour plots may be generated using the same data as theheat maps.

FIGS. 2 and 3 each shows a phase space volumetric object generated froma biophysical measurement of a subject determined to have significantcoronary artery disease in accordance with an illustrative embodiment.

Given that computed phase space tomographic images are rendered imagesof the phase space volumetric object from a specific vantage and/orview, a phase space volumetric object can also be referred to as acomputed phase space tomographic image. As shown in FIG. 2, each of thex-axis 202, y-axis 204, and z-axis 206 of the phase space volumetricobject includes a set of fractional derivative orders associated withthe fractional derivative operation performed on components of asubspace data set (e.g., the input data set, the model data set, or amodel of the low-energy frequency subspace data set). The fractionalderivative operation non-linearly preserves and enhances features of thesubspace data set in different frequency bands. To this end, longcardiac phase gradient signals, existing as high-dimensional data due tothe multiple acquisition leads, and exhibiting complex nonlinearvariability, can be efficiently captured by this modeling techniques.

As shown in the example of FIG. 2, values of one or more fractionalderivative orders are expressed in order at positions a₀ (208), a₁(210), a₂ (212), a₃ (214), a₄ (216), a₅ (218), and a₆ (220)corresponding to indexed values of the low-energy frequency subspacedata set. The orders are arranged, in some embodiments, in a sequence ofascending or descending values and are equally spaced apart from oneanother along each respective axis (202, 204, 206).

In some embodiments, the fractional derivative orders are pre-definedand may correspond to frequencies of electrical conduction events of theheart including those associated with activation (e.g., ventricularand/or atrio depolarization) of the various chambers and recovery (i.e.,ventricular and/or atrio repolarization).

Indeed, the phase space volumetric object 112 provides a framework ofaggregating multiple analyses (i.e., fractional derivative transform andlow-energy frequency subspace analysis) of subspace data set thatnon-linearly preserves and enhances features in the low-energy frequencysubspace data set in different frequency bands and representing theseanalyses, and/or the results thereof, as a three-dimensional volumetricobject. In addition to being visually more distinct when rendered, it isobserved that various topologic or geometric characteristics of thephase space volumetric object 112 can be readily extracted and/ordetermined to be used as predictors of presence or non-presence ofsignificant coronary artery disease. In some embodiments, the extractedtopologic or geometric characteristics include an assessed volume of thephase space volumetric object 112. In other embodiments, views of thephase space volumetric object can be presented as computed tomographicimages that can be directly presented to a physician for evaluation.

In some embodiments, different fractional derivative orders may be usedfor different axes of the phase space model. In some embodiments, inputsfrom different sensor types may be fused in a single phase space modelto which different sets of fractional derivative orders may be appliedfor each respective sensor type.

FIGS. 2 and 3 each shows a phase space volumetric object generated froma biophysical measurement of a subject known to be CAD positive—that is,the subject has been determined to have significant coronary arterydisease.

FIG. 4 shows a phase space volumetric object generated from abiophysical measurement of a subject known to be CAD negative—that is,the subject has been determined not to have significant coronary arterydisease. As shown, the volume of the phase space volumetric object 112of FIG. 2 or 3 associated with a CAD-positive subject is substantiallyhigher than that of the phase space volumetric object 112 of FIG. 4associated with a CAD-negative subject.

In some embodiments, the extracted topologic or geometriccharacteristics include a determination of whether the phase spacevolumetric object 112 includes certain shaped structures (e.g., arc oropen space). In some embodiments, the extracted topologic or geometriccharacteristics include a determination of whether the phase spacevolumetric object 112 includes a fragmentary volume (i.e., more than onecontiguous volume).

FIG. 5 shows a phase space volumetric object generated from ameasurement of a subject known to be CAD positive in which the object112 includes an arc structure 502 that forms an open space 504 in theobject 112.

As shown in FIG. 2, in addition to structural components, in someembodiments, the phase space volumetric object 112 is configured withcolor map information that corresponds to additional dimension ofanalysis. In some embodiments, each vertex has one or more color valuesthat are calculated as a variance between a modeled channel data set(e.g., X-axis data set, Y-axis data set, or Z-axis data set) a base-lineraw channel data set (e.g., corresponding X-axis data set, Y-axis dataset, or Z-axis data set). In some embodiments, the variance isdetermined by subtracting data points of the base-line raw channel dataset with the corresponding data points of the modeled channel data set.The modeled channel data set, in some embodiments, is based on a sparseapproximation of the base-line raw channel data set to generate areconstructed noiseless signal of the base-line raw channel data. Insome embodiments, each face of the phase space volumetric object 112 isassigned a face color value triangularly interpolated among neighboringbounding vertex color values (e.g., 3 bounding vertex colors).

Example Method to Construct a Phase Space Volumetric Object

FIG. 6 is an example method 600 of generating a phase space volumetricobject 112 by the non-invasive cardiac assessment system 110 inaccordance with an illustrative embodiment. The method 600 includesremoving (operation 602) a baseline wander from the raw differentialchannel signal of phase-gradient biophysical data set 108. In someembodiments, the raw differential channel signal are derived from sixsignals simultaneously sampled by the measurement system 102.

In some embodiments, six simultaneously sampled signals are capturedfrom a resting subject as the raw differential channel signal data setin which the signals embed the inter-lead timing and phase informationof the acquired signals, specific to the subject. Geometrical contrastarising from the interference in the phase plane of the depolarizationwave with the other orthogonal leads can be used which can facilitatesuperimposition of phase space information on a three-dimensionalrepresentation of the heart. Noiseless subspaces further facilitate theobservation of the phase of these waves. That is, the phase of theorthogonal leads carries the information about the structure andgenerates geometrical contrast in the image. Phase-contrast takesadvantage of the fact that different bioelectric structures havedifferent impedances, and so spectral and non-spectral conduction delaysand bends the trajectory of phase space orbit through the heart bydifferent amounts. These small changes in trajectory can be normalizedand quantified beat to beat and corrected for abnormal or poor leadplacement, and the normalized phase space integrals can be mapped to ageometric mesh for visualization.

In some embodiments, the raw differential channel signal data set isnormalized and baseline wander are removed using a modified movingaverage filter. For example, in some embodiments, the baseline wander isextracted from each of the raw differential channel signals using amedian filter with an order of 1500 milliseconds, smoothed with a 1-Hzlow-pass filter, and subtracted from the signals. The bias is thenremoved from the resulting signals by subtracting estimations of thesignals using maximums of probability densities calculated with a kernelsmoothing function. All of the signals may be divided by theirrespective interquartile ranges to complete the normalization process.In other embodiments, the baseline wander is removed using aphase-linear 2^(nd) order high-pass filter (e.g., a second-orderforward-reverse high-pass filter having a cut-off frequency at 0.67 Hz).The forward and reverse operation ensures that the resultingpre-processed biophysical-signal data set 118 is phase-linear. Otherphase-linear operations be used—e.g., based on wavelet filters, etc.

The method 600 then includes reconstructing (operation 604) a noiselessmodel signal by decomposing and selecting sets of candidate basisfunctions to create a sparse mathematical model. In some embodiments, aModified Matching Pursuit (MMP) algorithm is used to find a noiselessmodel of the raw differential channel signals. Other sparseapproximation algorithms can be used, including, and not limited to,evolvable mathematical models, symbolic regression, orthogonal matchingpursuit, LASSO, linear models optimized using cyclical coordinatedescent, orthogonal search, fast orthogonal search, and cyclicalcoordinate descent. In some embodiments, the reconstructing operation604 generates a model as a function with a weighted sum of basisfunctions in which basis function terms are sequentially appends to aninitially empty basis to approximate a target function while reducingthe approximation error.

The method 600 then includes selecting (operation 606) subspacecomponents (e.g., low energy frequency subspace components) from theselected basis functions and coefficients. The low-energy subspacecomponents comprises a model reconstructed by using only the X % lowmagnitude subset coefficients (frequency content) contributing least tothe modelling error. Low-energy subspace components, in someembodiments, includes higher order candidate terms that are laterselected, in the phase space coordinates, as part of the sparserepresentation of a signal. That is, the last 5 percent, 10 percent, 15percent, 20 percent, 25 percent, 30 percent of the candidate terms (asthe higher order candidate terms) last selected via the sparseapproximation is used. Other percentage values can be used. Thelow-energy frequency subspace components can be used to define the shapeof the three-dimensional point cloud of the phase space volumetricobject 112.

The method 600 then includes reconstructing (operation 608) apre-defined set of n^(th) order fractional derivative result set (e.g.,via a numeric fractional derivative operation) to generate, for example,color parameters for the three-dimensional point cloud defining, inpart, the phase space volumetric object 112. In some embodiments, thefractional derivative order is an irrational number. In someembodiments, more than one fractional derivative operation may beapplied with different fractional derivative orders. In someembodiments, the fractional derivative operation is based onGrünwald-Letnikov fractional derivative method. In some embodiments, thefractional derivative operation is based on the Lubich's fractionallinear multi-step method. In some embodiments, the fractional derivativeoperation is based on the fractional Adams-Moulton method. In someembodiments, the fractional derivative operation is based on theRiemann-Liouville fractional derivative method. In some embodiments, thefractional derivative operation is based on Riesz fractional derivativemethod. Other methods of performing a fractional derivative may be used.

The method 600 then includes, in some embodiments, performing (610)triangulation operation to generate surface features (i.e., face) of thepoint cloud. In some embodiments, Alpha Hull triangulation with apre-predetermined radius (a) is performed on the reconstructed noiselessmodel signals. In other embodiments, Delaunay triangulation, alphashapes, ball pivoting, Mesh generation, Convex Hull triangulation, andthe like, is used.

The method 600 then includes, in some embodiments, computing (612) oneor more values for each of the vertices in the point cloud. The vertexvalues, in some embodiments, are scaled over a presentable color range.The vertex values, in some embodiments, is a variance between a modeledchannel data set (e.g., X-axis data set, Y-axis data set, or Z-axis dataset) a base-line raw channel data set (e.g., corresponding X-axis dataset, Y-axis data set, or Z-axis data set). In some embodiments, thevariance is determined by subtracting data points of the base-line rawchannel data set with the corresponding data points of the modeledchannel data set. The modeled channel data set, in some embodiments, isbased on a sparse approximation of the base-line raw channel data set togenerate a reconstructed noiseless signal of the base-line raw channeldata. In some embodiments, each face of the phase space volumetricobject 112 is assigned a face color value triangularly interpolatedamong neighboring bounding vertex color values (e.g., 3 bounding vertexcolors).

In some embodiments, various views of the phase space volumetric object112 are captured for presentation as computed phase space tomographicimages, e.g., via a web portal, to a physician to assist the physicianin the assessment of presence or non-presence of significant coronaryartery disease. In some embodiments, the phase space volumetric objector the computed phase space tomographic images are assessed by a trainedneural network classifier configured to assess for presence ornon-presence of significant coronary artery disease. In someembodiments, the computed tomographic images are presented alongside theresults of a machine-generated predictions to assist in the physician inmaking a diagnosis.

In other embodiments, the phase space volumetric object 112 is analyzedin subsequent machine learning operations (e.g., image-based machinelearning operations or feature-based machine learning operations) todetermine the one or more coronary physiological parameters. In someembodiments, the assessment system 110 is configured to determine avolume metric (e.g., alpha hull volume) of the phase space volumetricobject 112. In some embodiments, the assessment system 110 is configuredto determine a number of distinct bodies (e.g., distinct volumes) of thegenerated phase space volumetric object 112. In some embodiments, theassessment system 110 is configured to assess a maximal color variation(e.g., color gradient) of the generated phase space volumetric object112. In some embodiments, all these features are assessed from phasespace volumetric object 112 as a mathematical feature.

In some embodiments, the mathematical features of the phase spacevolumetric object 112 are extracted along with hundreds of otherdistinct mathematical features that represent specific aspects of thebiophysical signals collected. A feature extraction engine of theassessment system 110 may extract each feature as a specificformula/algorithm. In some embodiments, when the feature extractionprocess is applied to an incoming biophysical signal, the output is amatrix of all calculated features which includes a list, for example, ofover hundreds of real numbers; one number per feature in which eachfeature represents one or more aspects of the signal's dynamical,geometrical, fractional calculus, chaotic, and/or topologicalproperties.

A machine learning algorithm (e.g., meta-genetic algorithm), in someembodiments, is used to generate predictors linking aspects of the phasespace model (e.g., pool of features) across a population of patientsrepresenting both positive (i.e., have disease) and negative (i.e., donot have disease) cases to detect the presence of myocardial tissueassociated with significant coronary artery disease. In someembodiments, the performances of the candidate predictors are evaluatedthrough a verification process against a previously unseen pool ofpatients. In some embodiments, the machine learning algorithm invokes ameta-genetic algorithm to automatically select a subset of featuresdrawn from a large pool. This feature subset is then used by an AdaptiveBoosting (AdaBoost) algorithm to generate predictors to diagnosesignificant coronary artery disease across a population of patientsrepresenting both positive and negative cases. The performances of thecandidate predictors are determined through verification against apreviously unseen pool of patients. A further description of theAdaBoost algorithm is provided in Freund, Yoav, and Robert E. Schapire,“A decision-theoretic generalization of on-line learning and anapplication to boosting,” European conference on computational learningtheory. Springer, Berlin, Heidelberg (1995), which is incorporated byreference herein in its entirety.

In some embodiments, the system 100 generates one or more images of arepresentation of the phase space volumetric object 112 in which thevertices, face triangulations, and vertex colors are presented. In someembodiments, multiple views of the representation is generated andincluded in a report. In some embodiments, the one or more images arepresented as a three-dimensional object that can be rotated, scaled,and/or panned based on user's inputs. Indeed, such presentation can beused to be assessed visually by a skilled operator to determine whethera subject has presence of non-presence of significant coronary arterydisease.

It can be seen from the example images presented in FIGS. 8-21 thatvisual features of the phase space volumetric object 112 can be used todistinguish between both presence/absence of significant CAD and alsodegrees of CAD. Specifically the presence of fragmentary volumes andcomplete arcs from the primary (central) body of the image appear to behighly indicative of significant CAD. The degree of coloration is alsoof interest, but harder to interpret manually. It can also been seenthat there is an emergent phenomena whereby subjects with blockages thatare classed as non-significant appear to be developing geometricfeatures prototypical of the arcs and fragmentation that indicate thepresence of significant CAD.

Experimental Results of Feature-Extracted Machine Learning

A Coronary Artery Disease—Learning Algorithm Development (CADLAD) Studyis currently being untaken that involves two distinct stages to supportthe development and testing of the machine-learned algorithms. In Stage1 of the CADLAD study, paired clinical data is being used to guide thedesign and development of the pre-processing, feature extraction andmachine learning steps. That is, the collected clinical study data issplit into three cohorts: Training (50%), validation (25%), andverification (25%). Similar to the steps described above for processingsignals from a patient for analysis, each signal is first pre-processed,to clean and normalize the data. Following these processes, a set offeatures are extracted from the signals in which each set of features ispaired with a representation of the true condition—for example, thebinary classification of the presence or absence of significant CAD. Thefinal output of this stage is a fixed algorithm embodied within ameasurement system. In Stage 2 of the CADLAD study, the machine-learnedalgorithms were used to provide a determination of significant CADagainst a pool of previously untested clinical data. The criteria fordisease was established as that defined in the American College ofCardiology (ACC) clinical guidelines, specifically as greater than 70%stenosis by angiography or less than 0.80 fraction-flow by flow wire.

In an aspect of the CADLAD study, an assessment system was developedthat automatically and iteratively explores combinations of features invarious functional permutations with the aim of finding thosecombinations which can successfully match a prediction based on thefeatures. To avoid overfitting of the solutions to the training data,the validation set is used as a comparator. Once candidate predictorshave been developed, they are then manually applied to a verificationdata set to assess the predictor performance against data that has notbeen used at all to generate the predictor. Provided that the data setsare sufficiently large, the performance of a selected predictor againstthe verification set will be close to the performance of that predictoragainst new data.

In an aspect of the CADLAD study, FIGS. 8-21 each shows an image of arepresentation of a phase space volumetric object 112 generated from asignal collected from a set of subjects in the CADLAD study inaccordance with an illustrative embodiment. The subjects were selectedat random from the CADLAD study and were evenly distributed across 4classes: (1) subjects with no reported arterial blockages; (2) subjectswith one or more blockages between 50% and 65%; (3) subjects with atleast one blockage greater than 70%; and (4) subjects with multipleblockages greater than 70%.

FIG. 8 shows an image of a representation of a phase space volumetricobject 112 generated from a signal collected from subject with noreported arterial blockage in accordance with an illustrativeembodiment. As can be seen, fractional derivative operations of a dataset acquired from a healthy subject (i.e., without coronary arterydisease) at most frequencies under study (i.e., fractional derivativeorder) yield minimal amplification of the underlying signal thateffectively produce a phase space volumetric object 112 with a low andcontiguous volume.

FIGS. 9, 10, and 11 each shows an image of a representation of a phasespace volumetric object 112 generated from a signal collected from asubject diagnosed with one or more reported arterial blockages onlybetween about 50% and about 65% in accordance with an illustrativeembodiment. In contrast to FIG. 8, the fractional derivative operationsof a data set acquired from a non-healthy subject (i.e., diagnosed withcoronary artery disease) at most, or some, frequencies under study(i.e., fractional derivative order) yield amplification of theunderlying signal that effectively produce a phase space volumetricobject 112 with a larger and/or non-contiguous/fragmented volume.

FIGS. 12, 13, 14, 15, and 16 each shows an image of a representation ofa phase space volumetric object 112 generated from a signal collectedfrom a subject diagnosed with at least one reported arterial blockagegreater than 70% in accordance with an illustrative embodiment.

FIGS. 17, 18, 19, 20, and 21 each shows an image of a representation ofa phase space volumetric object 112 generated from a signal collectedfrom a subject diagnosed with more than one reported arterial blockageeach greater than 70% in accordance with an illustrative embodiment.

Cardiac Phase Space Tomography

As noted above, computed tomographic images that the physician canthemselves interpret, can be produced based on the phase-spacevolumetric object. In some embodiments, the phase space volumetricobjects 112 are used to generate a set of two dimensional views as thecomputed phase space tomographic images which can be directlyinterpreted, e.g., by a physician or by a machine learned classifier toassess for presence or non-presence of significant coronary arterydisease. In certain implementations, a machine learned classifier hasbeen observed to achieve a ROC (receiver operating characteristics) of0.68 (0.49, 0.82) in which significant coronary artery disease isdefined as greater than 70% stenosis by angiography or less than 0.80fraction flow-by-flow wire.

FIGS. 22A, 22B, 22C, 22D, 22E, and 22F show a set of computedphase-space tomographic images 2202, 2204, 2206, 2208, 2210, 2212derived from six different views of the phase space volumetric object112 (shown as 112 a) associated with a healthy subject (i.e., a personassessed to not have significant coronary artery disease) in accordancewith an illustrative embodiment. Specifically, FIG. 22A shows a rightview (2202) of a phase space volumetric object 112 a, which alsocorresponds to the x-axis of the phase space volumetric object 112 a.FIG. 22B shows a left view (2204) of a phase space volumetric object 112a, which also corresponds to the other direction of the x-axis of thephase space volumetric object 112 a. FIG. 22C shows a front view (2206)of a phase space volumetric object 112 a, which also corresponds to thez-axis of the phase space volumetric object 112 a. FIG. 22D shows a backview (2208) of a phase space volumetric object 112 a, which alsocorresponds to the other direction along the z-axis of the phase spacevolumetric object 112 a. FIG. 22E shows a top view (2210) of a phasespace volumetric object 112 a, which also corresponds to the y-axis ofthe phase space volumetric object 112 a. FIG. 22F shows a bottom view(2212) of a phase space volumetric object 112 a, which also correspondsto the other direction along the y-axis of the phase space volumetricobject 112 a. As shown, the images are created from 30 seconds ofpatient signal, and a total of five images were created per patientusing non-overlapping sub-signals from the total 210 second available.

Neural Network Classification

The three-dimensional phase-space volumetric object or the computedphase-space tomographic images (e.g., 2202, 2204, 2206, 2208, 2210,2212) can be directly evaluated by a trained neural network classifierto determine presence or non-presence of significant coronary arterydisease. It is observed that a machine learned classifier can achieve aprediction having a ROC-AUC of 0.68 (0.49, 0.82). The characteristics ofthe development and test data sets used to train the machine learnedclassifier to produce this result is provided in table of FIG. 31.

In some embodiments, the neural network classifier may be a neuralnetwork trained on a set of grayscale tomographic images which arepaired with coronary angiography results assessed for presence andnon-presence of significant coronary artery disease. In someembodiments, a neural network-based nonlinear classifier is used. Insome embodiments, the neural network-based non-linear classifier isconfigured to map individual pixels from the generated tomographicimages to a binary CAD prediction. In some embodiments, the neuralnetwork's weights, which govern this mapping, is optimized usinggradient descent techniques.

FIGS. 23A, 23B, 23C, 23D, 23E, and 23F show outputted classification ofthe tomographic images of FIGS. 22A-22F for presence and non-presence ofsignificant coronary artery disease determined via a neural networkclassifier, in accordance with an illustrative embodiment. Each of thetomographic image of FIGS. 22A-22F are used as input to a neuralnetwork-based nonlinear classifier configured to map individual pixelsfrom the tomographic images to a binary CAD prediction. Here, theclassifier is configured to sweep a 4×4 moving window of white pixels(i.e., having a value of 1 in grayscale) over each respective image(e.g., 2202, 2204, 2206, 2208, 2210, 2212) with an output of the neuralnetwork being evaluated for each window position and its output beingrecorded. Because a given pixel in the resulting image is covered bymore than one moving windows (i.e., in that the window is larger than asingle pixel but moving one pixel at a time), each pixel in a heat mapis determined as an average/mean of each of the applicable movingwindow. Here, contour plots are generated using the same data as theheat maps.

FIGS. 24A, 24B, 24C, 24D, 24E, and 24F show classification of thetomographic images of FIGS. 22A-22F overlaid with a contour data set andheat map associated with the classifier in accordance with anillustrative embodiment. As shown in the tomographic images, yellow andgreen contours (white on the heat maps) show areas contributing to anegative prediction of presence of significant coronary artery disease,while purple contours (black on the heat maps) show areas that arecontributing to a positive prediction of presence of significantcoronary artery disease.

In some embodiments, more than one phase space volumetric objects 112are generated and evaluated from a single phase-gradient biophysicaldata set 108 acquired in a single acquisition session. For example, if aphase-gradient biophysical data set is acquired over about 210 seconds,and a set of phase space volumetric objects 112 is generated from about30 seconds of data, then multiple phase space volumetric objects 112(e.g., one to seven) could be generated and analyzed fromnon-overlapping portion of the phase-gradient biophysical data set.

In some embodiments, a neural network classifier containing a pluralityof hidden neurons (e.g., 15 neurons or more) with leaky rectified linearactivations is used. Dropout may be used between the hidden layer andthe final output neuron, in some embodiments, to prevent overfitting. L1and L2 regularization penalties may also be applied. Binary crossentropy may be used as a loss function, and optimization maybe performedusing a gradient-based Adam algorithm.

Table 1 shows an example set of parameter values for the neural network,which were determined empirically. Other neural network types andconfiguration can be used.

TABLE 1 Learning rate 1e⁻⁵ Alpha (for leaky rectified linearactivations) 0.3 Dropout 0.5 L1/L2 penalty 0.02 Clipnorm 1

FIGS. 25A, 25B, 25C, 25D, 25E, and 25F show only the contour data setand heat map data set of FIGS. 24A-24F in accordance with anillustrative embodiment.

FIGS. 26A, 26B, 26C, 26D, 26E, and 26F show computed phase-spacetomographic images derived from different views of the phase spacevolumetric object 112 and overlaid with the contour data set and heatmap data set generated from the neural network classifier of FIGS.25A-25F in accordance with an illustrative embodiment.

FIGS. 27A, 27B, 27C, 27D, 27E, and 27F show computed phase-spacetomographic images derived from different views of a phase spacevolumetric object 112 (shown as 112 b) associated with a subjectdiagnosed with significant coronary artery disease in accordance with anillustrative embodiment. The computed phase-space tomographic images areshown with contour data set and heat map data set generated from aneural network classifier applied to the computed phase-spacetomographic images.

FIGS. 28A, 28B, 28C, 28D, 28E, and 28F show outputted classification ofthe tomographic images of FIGS. 27A-27F for presence and non-presence ofsignificant coronary artery disease determined via a neural networkclassifier, in accordance with an illustrative embodiment.

FIGS. 29A, 29B, 29C, 29D, 29E, and 29F show example two-dimensionaloverlays superimposed over a three-dimensional volumetric object inaccordance with an illustrative embodiment. The two dimensional overlayare analogous to contours and are rendered in a three-dimensional spaceover the three-dimensional volumetric object to facilitate thevisualization of the contour and heat map information over thethree-dimensional volumetric object. Ovals and tori are not the onlyshapes possible for these overlays as other visualization elements canbe used. FIGS. 30A, 30B, 30C, 30D, 30E, and 30F show example threedimensional overlay superimposed over a three-dimensional volumetricobject in accordance with an illustrative embodiment. Different views ofthe three-dimensional volumetric objects superimposed with the 2Doverlay or the 3D overlay can be generated as computed phase-spacetomographic images.

FIGS. 32, 33, 34, 35, 36, 37, 38, and 39 show example graphical userinterface for a clinician web portal, or a report derived therefrom, toview and assess cardiac phase space tomographic images, in accordancewith an illustrative embodiment.

FIG. 32 shows a report with regions of myocardium at risk of significantcoronary artery disease highlighted on a 17 segment anatomical heartmap, in accordance with an illustrative embodiment. The subject here isdiagnosed with significant coronary artery disease. In FIG. 32, themachine-assessed ischemic burden of the subject is shown. The areasdesignated with myocardium at risk may be derived from the assessment ofpresence or non-presence of significant coronary disease. Furtherdescription is provided in U.S. application Ser. No. 15/712,104, whichis incorporated by reference herein in its entirety.

FIG. 33 shows example renderings of a three-dimensional volumetricobject associated with the data set used to generate the report of FIG.32, in accordance with an illustrative embodiment.

FIG. 34 shows another report with regions of myocardium at risk ofsignificant coronary artery disease highlighted on a 17 segmentanatomical heart map, in accordance with an illustrative embodiment. InFIG. 34, another presentation of the machine-assessed ischemic burden ofthe subject is shown.

FIG. 35 shows another report with regions of myocardium at risk ofsignificant coronary artery disease highlighted on a 17 segmentanatomical heart map, in accordance with an illustrative embodiment. InFIG. 35, yet another presentation of the machine-assessed ischemicburden of the subject is shown.

FIG. 36 shows a report of an example renderings of a three-dimensionalvolumetric object associated with the data set used to generate thereport of FIG. 32, in accordance with an illustrative embodiment. InFIG. 36, another presentation of the machine-assessed ischemic burden ofthe subject is shown in conjunction with the three-dimensionalvolumetric object.

FIG. 37 shows a report of an example renderings of a three-dimensionalvolumetric object associated with the data set used to generate thereport of FIG. 32, in accordance with an illustrative embodiment. InFIG. 37, yet another presentation of the machine-assessed ischemicburden of the subject is shown in conjunction with the three-dimensionalvolumetric object.

FIG. 38 shows a report of an example renderings of a three-dimensionalvolumetric object associated with the data set used to generate thereport of FIG. 32, in accordance with an illustrative embodiment. InFIG. 38, machine-assessed two-dimensional contour overlays correspondingto risk are presented. An interpretative key is provided.

FIG. 39 shows a report of an example renderings of a three-dimensionalvolumetric object associated with the data set used to generate thereport of FIG. 32, in accordance with an illustrative embodiment. InFIG. 39, machine-assessed three-dimensional contour overlayscorresponding to risk are presented. An interpretative key is provided.

Biopotential-Based Measurement Equipment and Sensors

Referring to the embodiment of FIG. 1, system 100 includesbiopotential-based measurement equipment 102 which, in some embodiments,is wide-band biopotential measuring equipment configured withbipotential sensing circuitries that, in the cardiography context,captures cardiac-related biopotential or electrophysiological signals ofa living subject such as a human as wide-band cardiac phase gradientsignals. Such equipment 102 may capture other biopotential orelectrophysiological signals, such as, e.g., cerebral biopotentialsignals and other biophysical signals discussed herein.

As described in U.S. Publication No. 2017/0119272 and in U.S.Publication No. 2018/0249960, each of which is incorporated by referenceherein in its entirety, the biopotential-based measurement equipment102, in some embodiments, is configured to capture unfilteredelectrophysiological signals such that the spectral component(s) of thesignals are not altered. That is, all of the captured signal, if not asignificant portion of the captured signal, includes, and does notexclude, components conventionally perceived/treated as and filtered outas noise (e.g., including those in the frequency range of greater thanabout 1 kHz). Further, the biopotential-based measurement equipment 102of FIG. 1 can capture, convert, and even analyze the collected wide-bandbiopotential signals without any filtering (via, e.g., hardwarecircuitry and/or digital signal processing techniques, etc.) thatotherwise can affect the phase linearity of the signal of interest inthe wide-band biopotential signals.

In some embodiments, the biopotential-based measurement equipment 102include wide-band equipment configured to capture one or more biosignalsof a subject, such as biopotential signals, in microvolt orsub-microvolt resolutions that are at, or significantly below, the noisefloor of conventional electrocardiographic and other biosignalacquisition instruments. In some embodiments, the wide-band biopotentialmeasuring equipment is configured to acquire and record wide-band phasegradient signals (e.g., wide-band cardiac phase gradient signals,wide-band cerebral phase gradient signals) that are simultaneouslysampled, in some embodiments, having a temporal skew or “lag” of lessthan about 1 μs, and in other embodiments, having a temporal skew or lagof not more than about 10 femtoseconds. Notably, the exemplified systemminimizes non-linear distortions (e.g., those that can be introduced viacertain filters) in the acquired wide-band phase gradient signal so asto not affect the information therein.

Phase Space Transformation and Analysis

As described in U.S. patent application Ser. No. 15/633,330, a phasespace analysis system is configured to generate a phase space map to beused to non-invasively measure myocardial ischemia based on featuresextracted from such phase space map.

FIG. 7 is a diagram of an exemplary method 700 of processing thephase-gradient biophysical data set 108 in accordance with anillustrative embodiment. The method 700 includes collecting andphase-gradient biophysical data set 108 to generate, via phase spaceanalysis techniques, a phase space dataset (shown as input data 716,“residue subspace” dataset 704 and “noise subspace” dataset 706). Thecharacteristics of the phase space data set (704, 706) and input dataset (716) may be extracted, in a feature extraction operation (e.g.,analysis steps 718, 722, 726) to determine geometric and dynamicproperties of the data set. These subspaces may include, but are notlimited to, complex subharmonic frequency (CSF) trajectory,quasi-periodic and chaotic subspaces, low/high energy subspaces, andfractional derivatives of the low/high energy subspaces. These subspacesare exemplars of the family of subspaces that characterize the dynamicsof the system, whether pathological or normal. In some embodiments, theextracted metrics are generated from the phase space volumetric object112 (shown as 112 a, 112 b, and 112 c) and generated from one or more ofthe phase space data sets (704, 706) and/or the input data set (716).

As shown in FIG. 7, one or more of the phase space data sets (704, 706)and/or the input data set (716), in some embodiments, are evaluated viafractional derivative operations to generate point cloud data set towhich faces are generated via triangulation. In some embodiments, one ormore color map data sets are generated for the determined vertex dataset. Metrics (e.g., extracted metrics 712 a, 712 b, 712 c) are assessedincluding a volume metric (e.g., alpha hull volume), a number ofdistinct bodies (e.g., distinct volumes), and/or a maximal colorvariation (e.g., color gradient) of the generated phase space volumetricobject 112.

The extracted metrics (712 a, 712 b, 712 c) can be subsequentlyevaluated via, e.g., nested non-linear functions 710 (associated withstenosis and/or FFR models) to estimate values 730 for a given subjectrelated to, e.g., regional FFR, the presence and/or degree of astenosis, ischemia, or presence or non-presence of significant coronaryartery disease, etc. In some embodiments, the values associated withregional FFR and the presence and/or degree of a stenosis and ischemiaare then mapped to point-cloud representation of a three-dimensionalmodel of the heart.

Analysis using phase space analysis techniques as described herein canfacilitate understanding of different bioelectric structures withinmammalian tissue, including but not limited to tissue in or associatedwith organs such as the brain or the heart. For example, various typesof cardiac tissue, particularly but not necessarily when such tissueis/are damaged or unhealthy, may exhibit different conductioncharacteristics, such as can be exhibited by differences in tissueimpedance. Indeed, these techniques can be used to understand spectraland non-spectral conduction delays and bends in the trajectory of thephase space orbit as it propagates through the heart. These smallchanges in trajectory can further be normalized and quantified on abeat-to-beat basis and corrected for abnormal or poor lead placement.The normalized phase space integrals can also be visualized on, ormapped to, a geometric mesh (e.g., a model of the heart) using a geneticalgorithm. In some embodiments, these phase space integrals are mappedto myocardial segments in the heart. In some embodiments, these mappedmyocardial segments can correspond to the 17-segments of the leftventricular model of the heart. Other number of myocardial segments maybe used.

Referring still to FIG. 7, three distinct phase space analyses areperformed to generate sets of metrics and variables (shown as steps 712a, 712 b, and 712 c). The metrics and variable are then used in thenon-linear functions (e.g., as shown in step 710) to generate regionalFFR estimation values, regional stenosis values, and regional ischemiavalues 730. Table 2 is an example output matrix of these values 122.

TABLE 2 Segment Vessel FFR Stenosis Ischemia 1 Left Main Artery (LMA)0.90 0.50 0.20 2 Proximal Left Circumflex Artery (Prox 0.85 0.60 0.30LCX) 3 Mid - Left Circumflex Artery (Mid LCX) 0.93 0.35 0.15 4 DistalLeft Circumflex Artery (Dist LCX) 1.00 0.00 0.00 5 Left PosteriorAtrioventricular (LPAV) 1.00 0.00 0.00 6 First Obtuse Marginal (OM1)0.60 0.95 0.72 7 Second Obtuse Marginal (OM2) 1.00 0.00 0.00 8 ThirdObtuse Marginal (OM3) 1.00 0.00 0.00 9 Proximal Left Anterior DescendingArtery 1.00 0.00 0.00 (Prox LAD) 10 Mid Left Anterior Descending Artery(Mid 1.00 0.00 0.00 LAD) 11 Distal Left Anterior Descending Artery 0.700.80 0.63 (Dist LAD) 12 LAD D1 0.00 0.00 0.75 13 LAD D2 0.00 0.00 0.0014 Proximal Right Coronary Artery (Prox 0.00 0.00 0.00 RCA) 15 Mid RightCoronary Artery (Mid RCA) 0.00 0.00 0.00 16 Distal Right Coronary Artery(Dist RCA) 0.00 0.00 0.18 17 Acute Marginal Brach Right of the Posterior0.00 0.00 0.00 Descending Artery (AcM R PDA)

As shown, Table 2 includes numerical values for a fractional flowreserve (FFR) parameter, an estimated stenosis parameter, and anestimated ischemia parameter for a plurality of (in this case, 17)segments corresponding to major vessels of a human heart. In someembodiments, matrix of the value 730 includes numerical values of afractional flow reserve (FFR) parameter, an estimated stenosisparameter, and an estimated ischemia parameter for a standardizedmyocardial segment map having 17 segments of the heart including theleft main artery (LMA), a proximal left circumflex artery (Prox LCX), amid-left circumflex artery (mid LCX), a distal left circumflex artery(Dist LCX), a LPAV, a first obtuse marginal (OM1), a second obtusemarginal (OM2), a third obtuse marginal (OM3), a proximal left anteriordescending artery (Prox LAD), a mid left anterior descending artery (MidLAD), a distal left anterior descending artery (Dist LAD), LAD D1, LADD2, a proximal right coronary artery (Prox RCA), a mid-right coronaryartery (Mid RCA), a distal right coronary artery (Dist RCA), and anacute marginal branch right of the posterior descending artery (AcM RPDA).

In Table 2, the parameter values for myocardial ischemia estimation,stenosis identification, and/or fractional flow reserve estimation areshown in a range of 0 to 1. Other scaling or ranges may be used, such asother non-numerical values to indicate a relative degree of theparameter of interest compared to a nominal standard.

Tables 3-6 show example non-linear functions used to generate FFRestimations for several segments corresponding to major vessels in theheart. In Table 3, an example function to determine a FFR estimation forthe left main artery (“FFR_LEFTMAIN”) is provided.

TABLE 3 FFR_LEFTMAIN = 0.128467341682411*noisevectorRz*atan2(Alpharatio,DensityV4)

As shown in Table 3, the FFR estimation for the left main artery isdetermined based on extracted metrics and/or variables such as aZ-component parameter associated with the noise subspace(“noisevectorRz”), a Alphahull ratio parameter (“Alpharatio”), and asignal density cloud volume 4 (“DensityV4”).

In Table 4, an example function to determine a FFR estimation for themid right coronary artery (“FFR_MIDRCA”) is provided.

TABLE 4 FFR_MIDRCA = 0.0212870065789474*noisevectorRy*Alpharatio*DensityV3

As shown in Table 4, the FFR estimation for the mid right coronaryartery is determined based on extracted metrics and/or variables such asa Y-component parameter associated with the noise subspace(“noisevectorRy”), the Alphahull ratio parameter (“Alpharatio”), and asignal density cloud volume 3 (“DensityV3”).

In Table 5, an example function to determine a FFR estimation for themid left artery descending (“FFR_MIDLAD”) is provided.

TABLE 5 FFR_MIDLAD = atan2(AspectRatio3, residueLevelMean)

As shown in Table 5, the FFR estimation for the mid left arterydescending is determined based on extracted metrics and/or variablessuch as a ratio of volume to surface area for cloud cluster 3(“AspectRatio3”) and a wavelet residue mean XYZ (“residueLevelMean”).

In Table 6, an example function to determine a FFR estimation for theproximal left circumflex artery (“FFR_PROXLCX”) is provided.

TABLE 6 FFR_PROXLCX = 0.408884581034257*atan2(residueLevelVolume+vectorcloud6, DensityV4)

As shown in Table 6, the FFR estimation for the proximal left circumflexartery is determined based on extracted metrics and/or variables such asa wavelet residue volume XYZ (“residueLevelVolume”), vector cloud 6volume (“vectorcloud6”), and a signal density cloud volume 4(“DensityV4”).

The output of the phase space analysis is then evaluated using machinelearning analysis to assess parameters associated with a presence and/ordegree of a disease or physiological characteristic (such as, e.g., inthe cardiovascular context, regional arterial flow characteristics). Insome embodiments, the machine learning analysis may use a library ofquantified FFR, stenosis, and ischemia data (e.g., data acquired from astudy of coronary arterial disease) in the assessment of the obtainedwide-band cardiac gradient signal data.

The output of a processor performing the analysis may then betransmitted to a graphical user interface, such as, e.g., a touchscreenor other monitor, for visualization. The graphical user interface, insome embodiments, is included in a display unit configured to displayvalues of any number of parameters discussed herein and elsewhere. Insome embodiments, the graphical user interface displays these data informats such as, e.g., a three-dimensional phase space plotrepresentation of the biopotential signal data and virtual biopotentialsignal data. In other embodiments, the data output of the processor isor may also be simultaneously or sequentially transmitted to one or morenon-graphical user interfaces (e.g., printout, command-line or text-onlyuser interface), directly to a database or memory device, processor,firmware, hardware and/or software for, e.g., later retrieval and/oradditional analysis, other machines that may include non-graphical userinterfaces for the display of such data, or combinations thereof. Anydevice, machine, or medium capable of receiving data and beinginterpreted by a human or machine or used for further processing iscontemplated and within the scope of the present disclosure.

A visualization engine may receive the determined arterial flowcharacteristics (such as FFR or stenosis values) and renders thecharacteristics onto a three dimensional visualization output. In someembodiments, the visualization engine provides, in a graphical userinterface (GUI), a system-level view of all of the arterial flowcharacteristics and their interactions. In some embodiments, the GUIpresents the cascading effects of upstream modifications to the arterialflow upon the downstream circulation. Further description of an examplevisualization engine is provided in U.S. Publication No. 2018/0078146,title “Method and System for Visualization of Heart Tissue at Risk”,which is incorporated by reference herein in its entirety.

Further examples of phase space and various processing that may be usedwith the exemplified method and system are described in: U.S. Pat. No.9,289,150, title “Non-invasive Method and System for CharacterizingCardiovascular Systems”; U.S. Pat. No. 9,655,536, title “Non-invasiveMethod and System for Characterizing Cardiovascular Systems”; U.S. Pat.No. 9,968,275, title “Non-invasive Method and System for CharacterizingCardiovascular Systems”; U.S. Pat. No. 8,923,958, title “System andMethod for Evaluating an Electrophysiological Signal”; U.S. Pat. No.9,408,543, title “Non-invasive Method and System for CharacterizingCardiovascular Systems and All-Cause Mortality and Sudden Cardiac DeathRisk”; U.S. Pat. No. 9,955,883, title “Non-invasive Method and Systemfor Characterizing Cardiovascular Systems and All-Cause Mortality andSudden Cardiac Death Risk”; U.S. Pat. No. 9,737,229, title “NoninvasiveElectrocardiographic Method for Estimating Mammalian Cardiac ChamberSize and Mechanical Function”; U.S. Pat. No. 10,039,468, title“Noninvasive Electrocardiographic Method for Estimating MammalianCardiac Chamber Size and Mechanical Function”; U.S. Pat. No. 9,597,021,title “Noninvasive Method for Estimating Glucose, GlycosylatedHemoglobin and Other Blood Constituents”; U.S. Pat. No. 9,968,265, title“Method and System for Characterizing Cardiovascular Systems From SingleChannel Data”; U.S. Pat. No. 9,910,964, title “Methods and Systems UsingMathematical Analysis and Machine Learning to Diagnose Disease”; U.S.Publication No. 2017/0119272, title “Method and Apparatus for Wide-BandPhase Gradient Signal Acquisition”; U.S. Publication No. 2018/0000371,title “Non-invasive Method and System for Measuring Myocardial Ischemia,Stenosis Identification, Localization and Fractional Flow ReserveEstimation”; U.S. Publication No. 2018/0078146, title “Method and Systemfor Visualization of Heart Tissue at Risk”; U.S. Publication No.2018/0249960, title “Method and System for Wide-band Phase GradientSignal Acquisition”; U.S. application Ser. No. ______, filedconcurrently herewith (having attorney docket no. 10321-025us1 andclaims priority to U.S. Provisional Appl. No. 62/611,826), title “Methodand System to Assess Disease Using Phase Space Volumetric Objects”; U.S.application Ser. No. 16/165,641, title “Methods and Systems ofDe-Noising Magnetic-Field Based Sensor Data of ElectrophysiologicalSignals”; U.S. application Ser. No. ______, filed concurrently herewith(having attorney docket no. 10321-032us1 and claims priority to U.S.Provisional Appl. No. 62/612,130), title “Method and System to AssessDisease Using Phase Space Tomography and Machine Learning”; U.S.application Ser. No. 15/653,433, title “Discovering Novel Features toUse in Machine Learning Techniques, such as Machine Learning Techniquesfor Diagnosing Medical Conditions”; U.S. application Ser. No.15/653,431, title “Discovering Genomes to Use in Machine LearningTechniques”, each of which is incorporated by reference herein in itsentirety.

Example Computing Device

FIG. 40 shows an exemplary computing environment in which exampleembodiments and aspects may be implemented.

The computing device environment is only one example of a suitablecomputing environment and is not intended to suggest any limitation asto the scope of use or functionality.

Numerous other general-purpose or special purpose computing devicesenvironments or configurations may be used. Examples of well-knowncomputing devices, environments, and/or configurations that may besuitable for use include, but are not limited to, personal computers,server computers, handheld or laptop devices, multiprocessor systems,microprocessor-based systems, network personal computers (PCs),minicomputers, mainframe computers, embedded systems, distributedcomputing environments that include any of the above systems or devices,and the like.

Computer-executable instructions, such as program modules, beingexecuted by a computer may be used. Generally, program modules includeroutines, programs, objects, components, data structures, etc. thatperform particular tasks or implement particular abstract data types.Distributed computing environments may be used where tasks are performedby remote processing devices that are linked through a communicationsnetwork or other data transmission medium. In a distributed computingenvironment, program modules and other data may be located in both localand remote computer storage media including memory storage devices.

With reference to FIG. 40, an exemplary system for implementing aspectsdescribed herein includes a computing device, such as computing device4000. In its most basic configuration, computing device 4000 typicallyincludes at least one processing unit 4002 and memory 4004. Depending onthe exact configuration and type of computing device, memory 4004 may bevolatile (such as random access memory (RAM)), non-volatile (such asread-only memory (ROM), flash memory, etc.), or some combination of thetwo. This most basic configuration is illustrated in FIG. 40 by dashedline 4006.

Computing device 4000 may have additional features/functionality. Forexample, computing device 4000 may include additional storage (removableand/or non-removable) including, but not limited to, magnetic or opticaldisks or tape. Such additional storage is illustrated in FIG. 40 byremovable storage 4008 and non-removable storage 4010.

Computing device 4000 typically includes a variety of computer readablemedia. Computer readable media can be any available media that can beaccessed by the device 4000 and includes both volatile and non-volatilemedia, removable and non-removable media.

Computer storage media include volatile and non-volatile, and removableand non-removable media implemented in any method or technology forstorage of information such as computer readable instructions, datastructures, program modules or other data. Memory 4004, removablestorage 4008, and non-removable storage 4010 are all examples ofcomputer storage media. Computer storage media include, but are notlimited to, RAM, ROM, electrically erasable program read-only memory(EEPROM), flash memory or other memory technology, CD-ROM, digitalversatile disks (DVD) or other optical storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other medium which can be used to store the desired information,and which can be accessed by computing device 4000. Any such computerstorage media may be part of computing device 4000.

Computing device 4000 may contain communication connection(s) 4012 thatallow the device to communicate with other devices. Computing device4000 may also have input device(s) 4014 such as a keyboard, mouse, pen,voice input device, touch input device, etc, singularly or incombination. Output device(s) 4016 such as a display, speakers, printer,vibratory mechanisms, etc. may also be included singularly or incombination. All these devices are well known in the art and need not bediscussed at length here.

It should be understood that the various techniques described herein maybe implemented in connection with hardware components or softwarecomponents or, where appropriate, with a combination of both.Illustrative types of hardware components that can be used includeGraphical Processing Units (GPUs), Field-programmable Gate Arrays(FPGAs), Application-specific Integrated Circuits (ASICs),Application-specific Standard Products (ASSPs), System-on-a-chip systems(SOCs), Complex Programmable Logic Devices (CPLDs), etc. The methods andapparatus of the presently disclosed subject matter, or certain aspectsor portions thereof, may take the form of program code (i.e.,instructions) embodied in tangible media, such as floppy diskettes,CD-ROMs, hard drives, or any other machine-readable storage mediumwhere, when the program code is loaded into and executed by a machine,such as a computer, the machine becomes an apparatus for practicing thepresently disclosed subject matter.

Although exemplary implementations may refer to utilizing aspects of thepresently disclosed subject matter in the context of one or morestand-alone computer systems, the subject matter is not so limited, butrather may be implemented in connection with any computing environment,such as a network or distributed computing environment. Still further,aspects of the presently disclosed subject matter may be implemented inor across a plurality of processing chips or devices, and storage maysimilarly be effected across a plurality of devices. Such devices mightinclude personal computers, network servers, handheld devices, andwearable devices, for example.

Although the subject matter has been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the subject matter defined in the appended claims is notnecessarily limited to the specific features or acts described above.Rather, the specific features and acts described above are disclosed asexample forms of implementing the claims.

Unless otherwise expressly stated, it is in no way intended that anymethod set forth herein be construed as requiring that its steps beperformed in a specific order. Accordingly, where a method claim doesnot actually recite an order to be followed by its steps or it is nototherwise specifically stated in the claims or descriptions that thesteps are to be limited to a specific order, it is no way intended thatan order be inferred, in any respect. This holds for any possiblenon-express basis for interpretation, including: matters of logic withrespect to arrangement of steps or operational flow; plain meaningderived from grammatical organization or punctuation; the number or typeof embodiments described in the specification.

While the methods and systems have been described in connection withcertain embodiments and specific examples, it is not intended that thescope be limited to the particular embodiments set forth, as theembodiments herein are intended in all respects to be illustrativerather than restrictive.

The methods, systems and processes described herein may be used generatestenosis and FFR outputs for use in connection with procedures such asthe placement of vascular stents within a vessel such as an artery of aliving (e.g., human) subject, and other interventional and surgicalsystem or processes. In one embodiment, the methods, systems andprocesses described herein can be configured to use the FFR/stenosisoutputs to determine and/or modify, intra operation, a number of stentsto be placed in a living (e.g., human), including their optimal locationof deployment within a given vessel, among others.

Examples of other biophysical signals that may be analyzed in whole, orin part, using the exemplary methods and systems include, but are notlimited to, an electrocardiogram (ECG) data set, an electroencephalogram(EEG) data set, a gamma synchrony signal data set; a respiratoryfunction signal data set; a pulse oximetry signal data set; a perfusiondata signal data set; a quasi-periodic biological signal data set; afetal ECG data set; a blood pressure signal; a cardiac magnetic fielddata set, and a heart rate signal data set.

The exemplary analysis can be used in the diagnosis and treatment ofcardiac-related pathologies and conditions and/or neurological-relatedpathologies and conditions, such assessment can be applied to thediagnosis and treatment (including, surgical, minimally invasive, and/orpharmacologic treatment) of any pathologies or conditions in which abiophysical signal is involved in any relevant system of a living body.One example in the cardiac context is the diagnosis of CAD and itstreatment by any number of therapies, alone or in combination, such asthe placement of a stent in a coronary artery, performance of anatherectomy, angioplasty, prescription of drug therapy, and/or theprescription of exercise, nutritional and other lifestyle changes, etc.Other cardiac-related pathologies or conditions that may be diagnosedinclude, e.g., arrhythmia, congestive heart failure, valve failure,pulmonary hypertension (e.g., pulmonary arterial hypertension, pulmonaryhypertension due to left heart disease, pulmonary hypertension due tolung disease, pulmonary hypertension due to chronic blood clots, andpulmonary hypertension due to other disease such as blood or otherdisorders), as well as other cardiac-related pathologies, conditionsand/or diseases. Non-limiting examples of neurological-related diseases,pathologies or conditions that may be diagnosed include, e.g., epilepsy,schizophrenia, Parkinson's Disease, Alzheimer's Disease (and all otherforms of dementia), autism spectrum (including Asperger syndrome),attention deficit hyperactivity disorder, Huntington's Disease, musculardystrophy, depression, bipolar disorder, brain/spinal cord tumors(malignant and benign), movement disorders, cognitive impairment, speechimpairment, various psychoses, brain/spinal cord/nerve injury, chronictraumatic encephalopathy, cluster headaches, migraine headaches,neuropathy (in its various forms, including peripheral neuropathy),phantom limb/pain, chronic fatigue syndrome, acute and/or chronic pain(including back pain, failed back surgery syndrome, etc.), dyskinesia,anxiety disorders, conditions caused by infections or foreign agents(e.g., Lyme disease, encephalitis, rabies), narcolepsy and other sleepdisorders, post-traumatic stress disorder, neurologicalconditions/effects related to stroke, aneurysms, hemorrhagic injury,etc., tinnitus and other hearing-related diseases/conditions andvision-related diseases/conditions.

What is claimed is:
 1. A method for non-invasively assessing presence ornon-presence of significant coronary artery disease, the methodcomprising: obtaining, by one or more processors, acquired data from ameasurement of one more biophysical signals of a subject, wherein theacquired data is derived from measurements acquired via noninvasiveequipment configured to measure properties of the heart; and generating,by the one or more processors, a set of tomographic images derived froma phase space model generated based on the acquired data, wherein atleast one of the phase space model comprises a plurality of faces and aplurality of vertices, wherein the plurality of vertices are defined, inpart, by a fractional subspace derivative operation and by low-energysubspace parameters generated directly or indirectly from the acquireddata; wherein the set of tomographic images are presented for anassessment of presence and/or non-presence of a disease.
 2. The methodof claim 1, comprising: determining, by the one or more processors, amachine-trained assessment of presence and/or non-presence ofsignificant coronary artery disease using a trained neural network-basednonlinear classifier.
 3. The method of claim 1, comprising: generating acontour data set for each tomographic image of the set of tomographicimages, wherein the contour data are presented for the assessment ofpresence and/or non-presence of significant coronary artery disease. 4.The method of claim 3, wherein the contour data set is generated by:sweeping, via the one or more processors, a moving window associatedwith the trained neural network-based nonlinear classifier on a pixel bypixel basis over, at least a portion of, a given tomographic image; andcombining, for a given pixel of the tomographic image, outputs of theswept moving window.
 5. The method claim 4, comprising: presenting, viathe display of the remote computing system, the generated contour dataset and a corresponding tomographic image used to generate the contourdata set, wherein the generated contour data set is rendered as anoverlay over the corresponding tomographic image.
 6. The method of claim4, wherein the generated contour data set comprises color map data, themethod further includes the step of presenting, via a display of theremote computing system, the set of tomographic images in conjunctionwith the generated contour data set.
 7. The method of claim 1, whereinvertices and faces of the generated phase space model comprises colordata, and wherein the step of generating the tomographic imagescomprising converting the generated phase space model to greyscale. 8.The method of claim 1, wherein the tomographic images are generated by:generating a plurality of images corresponding to a plurality oforientation of the generated phase space model, wherein the image aregenerated at a first image resolution; converting the plurality ofimages to a second image resolution, wherein the second image resolutionis different from the first image resolution.
 9. The method of claim 1,comprising: determining, by the one or more processors, one or morecoronary physiological parameters of the subject selected from the groupconsisting of a fractional flow reserve estimation, a stenosis value,and a myocardial ischemia estimation, based on the generated phase spacemodel (e.g., and causing, by the one or more processors, output of theone or more coronary physiological parameters (e.g., in a report, adisplay, instrumentation output, etc.)).
 10. The method of claim 1,wherein parameters associated with generated phase space model are usedin subsequent machine learning operations to determine the one or morecoronary physiological parameters.
 11. The method of claim 1, whereinthe generated phase space model comprises a three-dimensional objectdefined by the plurality of faces and a plurality of vertices.
 12. Themethod of claim 11, wherein the plurality of vertices are generated as apoint cloud in 3D space, wherein each point in the point cloud has avalue associated with a fractional order of a fractional subspacederivative operation of the low-energy subspace parameters.
 13. Themethod of claim 12, wherein each fractional order of the fractionalsubspace derivative operation is predetermined.
 14. The method of claim13, wherein each of the plurality of vertices or each of the pluralityof faces comprises one or more attribute parameters.
 15. The method ofclaim 14, where the each of the plurality of vertices or each of theplurality of faces comprises one or more color attribute parameters,where at least one of the one or more color attribute parameters isassociated with a variance of a modeled channel signal generated from amodel-derived construction of the acquired data subtracted from abaseline-removed raw channel of the acquired data.
 16. The method ofclaim 1, wherein the plurality of faces are generated from atriangulation operation of the plurality of vertices, wherein theplurality of faces are generated from the triangulation operation, thetriangulation operation being selected from the group consisting ofDelaunay triangulation, Mesh generation, Alpha Hull triangulation, andConvex Hull triangulation.
 17. The method of claim 16, wherein at leastone of the one or more face color attribute parameters is a triangularinterpolation among bounding vertex attribute parameters.
 18. The methodof claim 12, wherein the fractional order is a rational number or anirrational number associated with one or more linear and/or non-lineardynamic response of the heart.
 19. The method of claim 1, furthercomprising: removing, by the one or more processors, a baselinewandering trend from the acquired data prior to generating the phasespace model; and performing a model-derived reconstruction operation ofthe acquired data to generate the low-energy subspace parameters, thelow-energy subspace parameters comprising a plurality of basis functionsand coefficients, wherein the low-energy subspace parameters consist oflow-energy subsets of plurality of basis functions and coefficients,wherein the low-energy subsets of plurality of basis functions andcoefficients are selected from the group consisting of: about 1% ofplurality of basis functions and coefficients associated with low energyfrequency subspace; about 5% of plurality of basis functions andcoefficients associated with low energy frequency subspace; about 10% ofplurality of basis functions and coefficients associated with low energyfrequency subspace; about 15% of plurality of basis functions andcoefficients associated with low energy frequency subspace; about 20% ofplurality of basis functions and coefficients associated with low energyfrequency subspace; and about 25% of plurality of basis functions andcoefficients associated with low energy frequency subspace, and whereinthe model-derived reconstruction operation generates over 100 basisfunctions and coefficients for a given acquired data.
 20. The method ofclaim 1, wherein the parameters associated with generated phase spacemodel are associated with geometric properties of the generated one ormore phase space models, wherein the parameters associated withgenerated phase space model are associated with geometric properties ofthe generated one or more phase space models selected from the groupconsisting of volume, number of distinct bodies, and color gradient. 21.The method of claim 1 comprising: causing, by the one or moreprocessors, generation of a visualization of generated phase spacevolumetric object as a three-dimensional object, wherein thethree-dimensional object is rendered and displayed at a display of acomputing device or a report
 22. The method of claim 1, furthercomprising: extracting a first set of morphologic features of thegenerated phase space model, wherein the first set of extractedmorphologic features include parameters selected from the groupconsisting of a 3D volume value, a void volume value, a surface areavalue, a principal curvature direction value, and a Betti number value.23. The method of claim 1 further comprising: dividing the generatedphase space model into a plurality of segments each comprisingnon-overlapping portions of the generated phase space model; andextracting a set of morphologic features of each of the plurality ofsegments, wherein the second set of extracted morphologic featuresincludes parameters selected from the group consisting of a 3D volumevalue, a void volume value, a surface area value, a principal curvaturedirection value, and a Betti number value, wherein the plurality ofsegments comprise a number of segments selected from the groupconsisting of 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,19, and
 20. 24. The method of claim 1, wherein the acquired data areacquired as one or more wide-band gradient signals simultaneously fromthe subject via at least one electrode, wherein at least one of one ormore wide-band gradient signals comprise a high-frequency time seriesdata that is spectrally unmodified prior to the processing in thephase-space analysis and, wherein the one or more wide-band gradientsignals comprise cardiac frequency information at a frequency selectedfrom the group consisting of about 1 kHz, about 2 kHz, about 3 kHz,about 4 kHz, about 5 kHz, about 6 kHz, about 7 kHz, about 8 kHz, about 9kHz, about 10 kHz, and greater than 10 kHz.
 25. A system comprising: aprocessor; and a memory having instructions thereon, wherein theinstructions when executed by the processor, cause the processor to:obtain acquired data from a measurement of one more biophysical signalsof a subject, wherein the acquired data is derived from measurementsacquired via noninvasive equipment configured to measure properties ofthe heart; and generate a set of tomographic images derived from a phasespace model generated based on the acquired data, wherein at least oneof the phase space model comprises a plurality of faces and a pluralityof vertices, wherein the plurality of vertices are defined, in part, bya fractional subspace derivative operation and by low-energy subspaceparameters generated directly or indirectly from the acquired data;wherein the set of tomographic images are presented for an assessment ofpresence and/or non-presence of a disease.
 26. A non-transitory computerreadable medium having instructions stored thereon, wherein execution ofthe instructions, cause the processor to: obtain acquired data from ameasurement of one more biophysical signals of a subject, wherein theacquired data is derived from measurements acquired via noninvasiveequipment configured to measure properties of the heart; and generate aset of tomographic images derived from a phase space model generatedbased on the acquired data, wherein at least one of the phase spacemodel comprises a plurality of faces and a plurality of vertices,wherein the plurality of vertices are defined, in part, by a fractionalsubspace derivative operation and by low-energy subspace parametersgenerated directly or indirectly from the acquired data; wherein the setof tomographic images are presented for an assessment of presence and/ornon-presence of a disease.